检验线性分类器是否真能区分两类样本，避免误判随机效应。
Statistical Verification of Linear Classifiers
- 基于同质性检验判断线性分类器是否有效捕捉类别差异。
- 在二维正态分布下，检验的p值上界实验验证高度准确。
- 发现IGFBP6和ELOVL5基因与乳腺癌复发显著相关。
我们提出一种与线性可分性密切相关的同质性检验方法，可用于判断线性分类器是仅由随机噪声驱动，还是真正捕捉了两类之间的差异。研究重点在于为该检验在二维样本上的p值建立上界。对于正态分布样本，实验表明该上界具有极高准确性。利用此上界，我们评估了用于检测雌激素受体阳性乳腺癌复发的基因对表达分类器，结果确认了IGFBP6和ELOVL5基因在此过程中的显著作用。
原文摘要 · Abstract (English)
We propose a homogeneity test closely related to the concept of linear separability between two samples. Using the test one can answer the question whether a linear classifier is merely ``random'' or effectively captures differences between two classes. We focus on establishing upper bounds for the test's \emph{p}-value when applied to two-dimensional samples. Specifically, for normally distributed samples we experimentally demonstrate that the upper bound is highly accurate. Using this bound, we evaluate classifiers designed to detect ER-positive breast cancer recurrence based on gene pair expression. Our findings confirm significance of IGFBP6 and ELOVL5 genes in this process.
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